{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src='http://hilpisch.com/taim_logo.png' width=\"350px\" align=\"right\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Artificial Intelligence in Finance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data-Driven Finance (b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dr Yves J Hilpisch | The AI Machine\n",
    "\n",
    "http://aimachine.io | http://twitter.com/dyjh"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Debunking Central Assumptions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Normality"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Sample Data Sets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from pylab import plt, mpl\n",
    "np.random.seed(100)\n",
    "plt.style.use('seaborn')\n",
    "mpl.rcParams['savefig.dpi'] = 300\n",
    "mpl.rcParams['font.family'] = 'serif'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 10000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "snrn = np.random.standard_normal(N)\n",
    "snrn -= snrn.mean()  # moment matching\n",
    "snrn /= snrn.std()  # moment matching"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.0"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "round(snrn.mean(), 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "round(snrn.std(), 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 6))\n",
    "plt.hist(snrn, bins=35);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "numbers = np.ones(N) * 1.5\n",
    "split = int(0.25 * N)\n",
    "numbers[split:3 * split] = -1\n",
    "numbers[3 * split:4 * split] = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "numbers -= numbers.mean()\n",
    "numbers /= numbers.std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "round(numbers.mean(), 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "round(numbers.std(), 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 6))\n",
    "plt.hist(numbers, bins=35);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "import scipy.stats as scs\n",
    "import statsmodels.api as sm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def dN(x, mu, sigma):\n",
    "    ''' Probability density function of a normal random variable x.\n",
    "    '''\n",
    "    z = (x - mu) / sigma\n",
    "    pdf = np.exp(-0.5 * z ** 2) / math.sqrt(2 * math.pi * sigma ** 2)\n",
    "    return pdf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def return_histogram(rets, title=''):\n",
    "    ''' Plots a histogram of the returns.\n",
    "    '''\n",
    "    plt.figure(figsize=(10, 6))\n",
    "    x = np.linspace(min(rets), max(rets), 100)\n",
    "    plt.hist(np.array(rets), bins=50,\n",
    "             density=True, label='frequency')\n",
    "    y = dN(x, np.mean(rets), np.std(rets))\n",
    "    plt.plot(x, y, linewidth=2, label='PDF')\n",
    "    plt.xlabel('log returns')\n",
    "    plt.ylabel('frequency/probability')\n",
    "    plt.title(title)\n",
    "    plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "return_histogram(snrn)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "return_histogram(numbers)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "def return_qqplot(rets, title=''):\n",
    "    ''' Generates a Q-Q plot of the returns.\n",
    "    '''\n",
    "    fig = sm.qqplot(rets, line='s', alpha=0.5)\n",
    "    fig.set_size_inches(10, 6)\n",
    "    plt.title(title)\n",
    "    plt.xlabel('theoretical quantiles')\n",
    "    plt.ylabel('sample quantiles')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "return_qqplot(snrn)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "return_qqplot(numbers)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def print_statistics(rets):\n",
    "    print('RETURN SAMPLE STATISTICS')\n",
    "    print('---------------------------------------------')\n",
    "    print('Skew of Sample Log Returns {:9.6f}'.format(\n",
    "                scs.skew(rets)))\n",
    "    print('Skew Normal Test p-value   {:9.6f}'.format(\n",
    "                scs.skewtest(rets)[1]))\n",
    "    print('---------------------------------------------')\n",
    "    print('Kurt of Sample Log Returns {:9.6f}'.format(\n",
    "                scs.kurtosis(rets)))\n",
    "    print('Kurt Normal Test p-value   {:9.6f}'.format(\n",
    "                scs.kurtosistest(rets)[1]))\n",
    "    print('---------------------------------------------')\n",
    "    print('Normal Test p-value        {:9.6f}'.format(\n",
    "                scs.normaltest(rets)[1]))\n",
    "    print('---------------------------------------------')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RETURN SAMPLE STATISTICS\n",
      "---------------------------------------------\n",
      "Skew of Sample Log Returns  0.016793\n",
      "Skew Normal Test p-value    0.492685\n",
      "---------------------------------------------\n",
      "Kurt of Sample Log Returns -0.024540\n",
      "Kurt Normal Test p-value    0.637637\n",
      "---------------------------------------------\n",
      "Normal Test p-value         0.707334\n",
      "---------------------------------------------\n"
     ]
    }
   ],
   "source": [
    "print_statistics(snrn)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RETURN SAMPLE STATISTICS\n",
      "---------------------------------------------\n",
      "Skew of Sample Log Returns  0.689254\n",
      "Skew Normal Test p-value    0.000000\n",
      "---------------------------------------------\n",
      "Kurt of Sample Log Returns -1.141902\n",
      "Kurt Normal Test p-value    0.000000\n",
      "---------------------------------------------\n",
      "Normal Test p-value         0.000000\n",
      "---------------------------------------------\n"
     ]
    }
   ],
   "source": [
    "print_statistics(numbers)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Real Financial Returns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "raw = pd.read_csv('http://hilpisch.com/aiif_eikon_eod_data.csv',\n",
    "                  index_col=0, parse_dates=True).dropna()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "rets = np.log(raw / raw.shift(1)).dropna()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "symbol = '.SPX'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "return_histogram(rets[symbol].values, symbol)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "return_qqplot(rets[symbol].values, symbol)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "symbols = ['.SPX', 'AMZN.O', 'EUR=', 'GLD']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      ".SPX\n",
      "=============================================\n",
      "RETURN SAMPLE STATISTICS\n",
      "---------------------------------------------\n",
      "Skew of Sample Log Returns -0.497160\n",
      "Skew Normal Test p-value    0.000000\n",
      "---------------------------------------------\n",
      "Kurt of Sample Log Returns  4.598167\n",
      "Kurt Normal Test p-value    0.000000\n",
      "---------------------------------------------\n",
      "Normal Test p-value         0.000000\n",
      "---------------------------------------------\n",
      "\n",
      "AMZN.O\n",
      "=============================================\n",
      "RETURN SAMPLE STATISTICS\n",
      "---------------------------------------------\n",
      "Skew of Sample Log Returns  0.135268\n",
      "Skew Normal Test p-value    0.005689\n",
      "---------------------------------------------\n",
      "Kurt of Sample Log Returns  7.344837\n",
      "Kurt Normal Test p-value    0.000000\n",
      "---------------------------------------------\n",
      "Normal Test p-value         0.000000\n",
      "---------------------------------------------\n",
      "\n",
      "EUR=\n",
      "=============================================\n",
      "RETURN SAMPLE STATISTICS\n",
      "---------------------------------------------\n",
      "Skew of Sample Log Returns -0.053959\n",
      "Skew Normal Test p-value    0.268203\n",
      "---------------------------------------------\n",
      "Kurt of Sample Log Returns  1.780899\n",
      "Kurt Normal Test p-value    0.000000\n",
      "---------------------------------------------\n",
      "Normal Test p-value         0.000000\n",
      "---------------------------------------------\n",
      "\n",
      "GLD\n",
      "=============================================\n",
      "RETURN SAMPLE STATISTICS\n",
      "---------------------------------------------\n",
      "Skew of Sample Log Returns -0.581025\n",
      "Skew Normal Test p-value    0.000000\n",
      "---------------------------------------------\n",
      "Kurt of Sample Log Returns  5.899701\n",
      "Kurt Normal Test p-value    0.000000\n",
      "---------------------------------------------\n",
      "Normal Test p-value         0.000000\n",
      "---------------------------------------------\n"
     ]
    }
   ],
   "source": [
    "for sym in symbols:\n",
    "    print('\\n{}'.format(sym))\n",
    "    print(45 * '=')\n",
    "    print_statistics(rets[sym].values)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear Relationships"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "r = 0.005"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "market = '.SPX'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "res = pd.DataFrame()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "for sym in rets.columns[:4]:\n",
    "    for year in range(2010, 2019):\n",
    "        rets_ = rets.loc[f'{year}-01-01':f'{year}-12-31']\n",
    "        muM = rets_[market].mean() * 252\n",
    "        cov = rets_.cov().loc[sym, market]\n",
    "        var = rets_[market].var()\n",
    "        beta = cov / var\n",
    "        rets_ = rets.loc[f'{year + 1}-01-01':f'{year + 1}-12-31']\n",
    "        muM = rets_[market].mean() * 252\n",
    "        mu_capm = r + beta * (muM - r)\n",
    "        mu_real = rets_[sym].mean() * 252\n",
    "        res = res.append(pd.DataFrame({'symbol': sym,\n",
    "                                       'beta': beta,\n",
    "                                       'mu_capm': mu_capm,\n",
    "                                       'mu_real': mu_real},\n",
    "                                      index=[year + 1]),\n",
    "                        sort=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import r2_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "reg = np.polyfit(res['beta'], res['mu_capm'], deg=1)\n",
    "res['mu_capm_ols'] = np.polyval(reg, res['beta'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.09272355783573516"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r2_score(res['mu_capm'], res['mu_capm_ols'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "res.plot(kind='scatter', x='beta', y='mu_capm', figsize=(10, 6))\n",
    "x = np.linspace(res['beta'].min(), res['beta'].max())\n",
    "plt.plot(x, np.polyval(reg, x), 'g--', label='regression')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "reg = np.polyfit(res['beta'], res['mu_real'], deg=1)\n",
    "res['mu_real_ols'] = np.polyval(reg, res['beta'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.04466919444752959"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r2_score(res['mu_real'], res['mu_real_ols'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "res.plot(kind='scatter', x='beta', y='mu_real', figsize=(10, 6))\n",
    "x = np.linspace(res['beta'].min(), res['beta'].max())\n",
    "plt.plot(x, np.polyval(reg, x), 'g--', label='regression')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src='http://hilpisch.com/taim_logo.png' width=\"350px\" align=\"right\">\n",
    "\n",
    "<br><br><br><a href=\"http://tpq.io\" target=\"_blank\">http://tpq.io</a> | <a href=\"http://twitter.com/dyjh\" target=\"_blank\">@dyjh</a> | <a href=\"mailto:ai@tpq.io\">ai@tpq.io</a>"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
